It potentially supports people discussion complex "wicked" problems like those frequent in politics in a way where controversy and disagreement can lead to collaborative construction of a shared knowledge map.
There are limits discussed in the book where people in politics may not want to participate in IBIS sessions because they don't want their private agendas exposed or challenged.
Ultimately the hope in reasonably healthy organizations is to find out what feasible solutions have the greatest buy-in from the group to make a decision to move forward with them.
Of course, you can also use IBIS tools just by yourself -- but that may miss out on some of the group's collective knowledge and wisdom.
Here is an example of Dialogue Mapping by someone using IBIS to dialogue map the "Lord of the Rings":
"Dialogue Mapping The Lord Of The Rings with Paul Culmsee & Nick Martin"